Evidence about Bubble Mechanisms: Precipitating Event, Feedback Trading, and Social Contagion *

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1 Evidence about Bubble Mechanisms: Precipitating Event, Feedback Trading, and Social Contagion * Neil D. Pearson University of Illinois at Urbana-Champaign Zhishu Yang School of Economics and Management, Tsinghua University Qi Zhang Durham University Business School April 1, 2017 Abstract Shiller s feedback loop theory of bubbles involves three elements: a precipitating event that causes an increase in prices, positive feedback trading, and social contagion that draws in new investors. We use brokerage account records from a large Chinese stock brokerage firm to show that all three components of the Shiller feedback loop are found during the Chinese put warrants bubble. An increase in the stock transaction tax made warrants relatively more attractive for speculative trading and was the precipitating event for the extreme phase of the bubble, causing immediate sharp increases in trading by new and existing investors and a jump in warrant prices. Hazard rate regressions show that there was positive feedback trading, and the period of heavy feedback trading coincided with the extreme phase of the bubble following the increase in the transaction tax. Proxies for social contagion explain the entry of new investors, and estimates of the trading volume due to feedback trading and the numbers of new investors drawn in by social contagion explain the size of the bubble. JEL codes: G12, G13, G14, O16, P34 Key words: Speculative bubble, feedback loop, precipitating event, feedback trading, social contagion. * This research is supported by a grant from the NSFC (Project Number: ). We gratefully thank Shi Gu and Yang Zhao for excellent research assistance, and thank Efraim Benmelech, Pengjie Gao, Bing Han, Zhiguo He, David Hirshleifer, Robert J. Shiller, Qiping Xu and participants at the 2016 China Financial Research Conference, 2016 Tsinghua Finance Symposium, 2016 Research in Behavioural Finance Conference, 2016 Miami Behavioral Finance Conference, KAIST, Nanjing University, University of Newcastle, and Case Western Reserve University for helpful comments. Send correspondence to Neil Pearson, University of Illinois at Urbana-Champaign, Department of Finance, 340 Wohlers Hall, 1206 South Sixth Street, Champaign, IL 61820; telephone pearson2@illinois.edu.

2 Evidence about Bubble Mechanisms: Precipitating Event, Feedback Trading, and Social Contagion Abstract Shiller s feedback loop theory of bubbles involves three elements: a precipitating event that causes an increase in prices, positive feedback trading, and social contagion that draws in new investors. We use brokerage account records from a large Chinese stock brokerage firm to show that all three components of the Shiller feedback loop are found during the Chinese put warrants bubble. An increase in the stock transaction tax made warrants relatively more attractive for speculative trading and was the precipitating event for the extreme phase of the bubble, causing immediate sharp increases in trading by new and existing investors and a jump in warrant prices. Hazard rate regressions show that there was positive feedback trading, and the period of heavy feedback trading coincided with the extreme phase of the bubble following the increase in the transaction tax. Proxies for social contagion explain the entry of new investors, and estimates of the trading volume due to feedback trading and the numbers of new investors drawn in by social contagion explain the size of the bubble. JEL codes: G12, G13, G14, O16, P34 Key words: Speculative bubble, feedback loop, precipitating event, feedback trading, social contagion.

3 1. Introduction Shiller s extensive writings about speculative asset price bubbles discuss how three components combine to create and reinforce bubbles (see for example, Shiller 1995, 2008, 2015). 1 First, a precipitating event causes an increase in prices. This precipitating event need not be related to the assets fundamental values; for example, Shiller (2015; Chapter 4) argues that rapid growth in corporate earnings in 1994, 1995, and 1996 contributed to the initiation of the internet bubble of the late 1990s even though the earnings growth had little to do with the internet. Second, there is a positive feedback loop in which past price increases encourage investors to continue buying, creating further upward pressure on prices (Shiller 2015; Chapter 5). Third, social contagion draws in additional investors. In some places Shiller focuses on the role of the media in spreading stories about asset price increases (for example, Shiller 2015, Chapter 6), while in others he emphasizes the role of direct word of mouth communication, for example writing the single most important element to be reckoned in understanding this or any other speculative boom is the social contagion of boom thinking, mediated by the common observation of rapidly increasing prices (Shiller 2008, p. 41; see also Shiller 2015, Chapter 10). We use brokerage account records from a large Chinese stock brokerage firm to document that all three components of the Shiller feedback loop are found during the Chinese put warrants bubble, and that they were important contributors to the bubble. We identify the exogenous event that precipitated the extreme phase of the bubble, and the date on which this event occurred. The brokerage account records allow us to estimate hazard rate regressions that document positive feedback trading throughout the bubble, including its extreme phase. Using the results of hazard rate regressions that predict the reentry into the market of investors who have previously traded put warrants, we estimate the buying due to positive feedback trading during the bubble and find that it was positive and large following the precipitating event, exacerbating the extreme phase of the bubble. We also use the brokerage account records to construct proxies for social contagion similar to those used by Kaustia and Knüpfer (2012) and use the proxies to show that social 1 See also Case and Shiller (1988, 1994, 2003), Akerlof and Shiller (2009, Chapter 9), and Shiller (1984, 2003, 2007, 2009, 2011, 2014). Shiller (2015, p. 84) summarizes the feedback mechanism: Initial price increases lead to more price increases as the effects of the initial price increases feedback into yet higher prices through increased investor demand. This second round of price increase feeds back again into a third round, and then into a fourth, and so on. Thus the initial impact of the precipitating factors is amplified into much larger price increases than the factors themselves would have suggested. 1

4 contagion drives the entry of new investors. The estimated relation between the probability of entry and the returns of geographically proximate investors is convex, consistent with the prediction of the Han and Hirshliefer (2016) model of the social transmission of information. Finally, we show that the predicted trading volumes due to positive feedback trading and social contagion explain warrant price levels, especially during the extreme phase of the bubble. These results are the first direct evidence of the three components of Shiller s feedback loop in a large dataset of investor trades, and also the first to show that they explain the magnitude of a bubble. We believe that we are unique in documenting how feedback trading and social contagion interact with a precipitating event to drive a speculative bubble. The Chinese put warrants bubble occurred on the Shanghai and Shenzhen stock exchanges during Between November 2005 and June Chinese companies issued put warrants with maturities of between six months and two years. 2 These warrants gave their holders the right to sell the issuing companies stocks at predetermined strike prices during specified exercise periods. The boom in Chinese stock prices caused most of these put warrants to be so far out of the money that they were almost certain to expire worthless. Despite this, the put warrants traded very actively at non-trivial prices, leading many to interpret the warrant trading as a speculative bubble, and Xiong and Yu (2011) build a compelling case that it was a bubble. 3 Among other evidence and arguments, Xiong and Yu (2011) document that many of the put warrants traded at prices far in excess of estimates of their values computed using the Black- Scholes formula, some of the warrants at times traded at prices that exceeded their strike prices, and that toward the end of their lives, some put warrants traded at non-trivial prices even though they were certain to expire out-of-the money even if their underlying stocks traded limit down for every trading day until the warrants expiration dates. This speculative bubble is an interesting event to study for at least two reasons. First, we have access to the trading records of a large group of Chinese investors who traded the put warrants during the bubble. Using these trading records we are able to identify the exogenous event that precipitated the extreme phase of the bubble, and the investors subsequent warrant purchases. The trading records allow us to study how investors warrant purchases are related to covariates 2 There were also 36 call warrants. The first call warrant, on Baogang stock, was issued on August 22, In addition to Xiong and Yu (2011), researchers who have interpreted the put warrant trading as a speculative bubble and/or provided evidence that the put warrants were overvalued include Liao, Li, Zhang, and Zhu (2010), Chang, Luo, Shi, and Zhang (2013), Powers and Xiao (2014), and Liu, Zhang and Zhao (2016). 2

5 including the returns on the investors own previous warrant purchases and the warrant returns of other geographically proximate investors with whom the investors might have had social contact. Using empirical models estimated using the trading records, we construct estimates of the trading volume that can be attributed to feedback trading and social contagion and find that these estimates trading volumes explain warrant prices during the bubble. In contrast, most previous empirical research on bubbles has relied on aggregate market data such as prices, returns, and trading volumes or turnover (for example, Hong and Stein 2007, Mei, Scheinkman, and Xiong 2009, and Xiong and Yu 2011), surveys of comparatively small numbers of investors (for example, Case and Shiller 1988, 2003), or limited documentary evidence (for example, Garber 1989, 1990, 2000). 4 Second, due to Xiong and Yu (2011) one can be confident that the investor trades we study are bubble phenomenon and not some mixture of bubble behavior and rationally motivated trading based on fundamental information. For example, because the prices of Chinese put warrants cannot be rationalized in terms of fundamentals one can be confident that the relations between trades and lagged returns we estimate are not caused by rational learning or updating of beliefs about fundamental information. In contrast, most other bubbles are controversial, with serious scholars offering arguments that they were not bubbles. For example, Hall (2001) and Li and Xue (2009) argue that the run-up in the prices of technology stocks during can be explained by technology shocks and Bayesian updating of beliefs about possible future technology shocks. Garber (1989, 1990, 2000) has even offered explanations of the Dutch Tulipmania, the Mississippi Bubble, and South Sea Bubble in terms of fundamentals. Using the stock brokerage account records, we are able to identify that a tripling of the stamp duty (transaction tax) imposed on stock trades that was announced at midnight on May 30, 2007 and took effect immediately at the opening of trading on May 30 precipitated the extreme phase of the put warrants bubble, which began on May 30. Because warrants were exempt from the stamp duty it made warrants more attractive than stocks for short-term speculative trading and caused striking increases in the both entry of new investors into the warrant market and the reentry of investors who had previously traded warrants. Market data show a more than 12-fold increase in warrant turnover on May 30 and an average warrant return of 57.6%, followed by further large positive returns over the next 15 days. The differences between warrant prices and estimates of their fundamental values were much higher on and after May 30, 2007 than before. 4 An exception is Gong, Pan and Shi (2016) who use investor trade data for the Baogang call warrant. 3

6 Turning to the second element of the Shiller feedback loop, we use hazard rate regressions to show that, for the investors who have previously traded put warrants, the probability that they buy again is positively related to their previous put warrant returns. This positive feedback trading occurs throughout the warrants lives, including during the extreme bubble period. The combination of the positive coefficients on investors previous returns and the large price increases beginning on May 30, 2007 due to the increase in the stamp duty lead to a burst of positive feedback trading beginning on this date and continuing for more than a month, throughout the extreme phase of the bubble. We provide evidence of social contagion by following Kaustia and Knüpfer (2012) and using the brokerage firm data to construct, for each date and investor who has never previously traded warrant k, estimates of the lagged returns that geographically proximate investors have achieved by trading warrant k. The lagged returns of geographically proximate investors can provide evidence about social contagion because these are the other investors with whom a given investor is most likely to have social contact. We find that the cross-sectional average of the positive parts of the lagged returns of such same-branch investors and the interaction of the average of the positive parts with the numbers of such same-branch investors predict the numbers of investors who make their first purchases of warrant k on each date. The estimated relation between entry and lagged returns is convex, consistent with the prediction of the recent Han and Hirshleifer (2016) model of the social transmission of information about trading strategies. We further examine this issue by estimating an alternative specification in which the probability of entry depends on an exponential function of the previous returns and find additional support for the Han and Hirshleifer (2016) prediction. In addition to showing that the three components of the Shiller feedback loop are present in the data, we provide evidence that feedback trading and social contagion contributed to the bubble by reexamining the Xiong and Yu (2011) panel regressions showing that put warrant prices were positively correlated with volatility and turnover, consistent with the resale option theory. Specifically, we use the feedback hazard rate regressions and social contagion (linear) regressions to develop estimates of the trading volumes due to feedback trading and social contagion during each day of the Xiong and Yu (2011) zero fundamental period in which the fundamental values of the put warrants were close to zero. We then include these estimates as additional covariates 4

7 in the panel regressions estimated by Xiong and Yu (2011) and find that the estimates of buying due to feedback trading and social contagion explain put warrant prices. We are far from the first to consider positive feedback trading; there is a long literature on it, both theoretical and empirical, with notable contributions including Shiller (1984), De Long, Shleifer, Summers, and Waldmann (1990), Cutler, Poterba, and Summers (1990), Lakonishok, Shleifer, and Vishny (1992), Lakonishok, Shleifer, and Vishny (1994), and Daniel, Hirshleifer, and Subrahmanyam (1998). More recently, Kaustia and Knupfer (2008), Choi, Laibson, Madrian and Metrick (2009), and Malmendier and Nagel (2011) have proposed that personally experienced outcomes have important impacts on investment decisions, providing one possible mechanism by which feedback trading can arise. Similarly, a developing literature on social contagion (for example Hong, Kubik and Stein (2004, 2005) and Brown, Ivkovic, Smith and Weisbenner (2008)) provides evidence that investors are more likely to participate in the stock market when other geographically proximate investors do so, and recent theoretical work (Han and Hirshleifer 2016) provides a prediction about the relation between entry of new investors and the previous returns of other investors. Our contribution is not to study feedback trading and social contagion per se, but rather to document that they drove the put warrants bubble. The Shiller feedback loop is not the only theory of speculative asset price bubbles. Scheinkman and Xiong (2003) have proposed a resale option theory of overvaluation, and, as indicated above, Xiong and Yu (2011) present evidence that put warrant prices were correlated with volatility and turnover as predicted by the resale option theory. This theory or the related model of Hong, Scheinkman and Xiong (2006) has found support in other data (Hong, Scheinkman and Xiong 2006, Hong and Stein 2007, and Mei, Scheinkman, and Xiong 2009). Blanchard and Watson (1983), Allen and Gorton (1993), and Allen and Gale (2000) have proposed other theories of asset price bubbles. The various theories are not mutually exclusive, and our findings that the components of the Shiller feedback loop are found during the Chinese put warrants bubble and impacted warrant prices does not imply that other mechanisms such as the resale option theory did not also contribute to the bubble. In addition to Xiong and Yu (2011), several other papers explore possible causes of the overvaluation of Chinese warrants. Powers and Xiao (2014) find that estimates of the overvaluation of put warrants are correlated with measures of liquidity and volatility, consistent 5

8 with the resale option theory. They also find that the overvaluation is greater after the May 30, 2007 increase in the transaction tax, though they do not recognize that the tax change was the precipitating event that caused the extreme phase of the bubble and examine neither feedback trading nor social contagion. Gong, Pan and Shi (2016) provide evidence that the BaoGang call warrant was consistently overvalued, and use account level data to show that on most trading days a majority of purchases were made by investors who had never previously held the warrant and that the ratio of purchases by new investors to total purchases was contemporaneously correlated with changes in a measure of overvaluation. They interpret these results to mean that the bubble was created and sustained by new investors, but do not attempt to determine the factors that might cause new investors to buy the warrant. In summary, none of these papers provide evidence about any of the three elements of the Shiller feedback loop. The next section of the paper describes the data we use, focusing on the brokerage account records. Section 3 presents evidence that an exogenous shock that precipitated the extreme phase of the bubble occurred on May 30, 2007, and identifies the shock. Section 4 presents the results about positive feedback trading, while Section 5 presents regression results showing that social contagion contributed to the entry of new investors. Section 6 shows that estimates of the trading volume due to positive feedback trading and the number of new investors due to social contagion explain put warrant prices during the bubble, and Section 7 briefly concludes. 2. Data Description and Summary Statistics 2.1 Background The put warrants we study were created as part of the Chinese share structure reform initiated in In this reform, non-tradable shares held by management, the state, or other stateowned enterprises were made tradable. Because this was expected to adversely affect the prices of the tradeable shares held by investors, holders of non-tradable shares were required to compensate holders of tradable shares, usually with cash or additional shares. In a few cases the compensation included warrants, leading to the creation of 36 call warrants and the 18 put warrants that we study. In some cases additional warrants were subsequently issued by special purpose vehicles established by financial institutions. The warrants were listed on either the Shanghai or Shenzhen stock exchanges, and traded like stocks, with the difference that a warrant could be sold on the same day it was purchased. In contrast, a Chinese stock purchased on day t may not be sold until the next trading day t + 1, i.e. it 6

9 must be held for at least one overnight period in a practice referred to as t + 1 settlement. This difference from the trading of Chinese stocks enabled intraday speculative trading in the warrants and made it possible for the put warrants to have extremely high trading volumes, and they sometimes did. One might also hypothesize that this contributed to the bubble in the prices of put warrants. An important way in which the warrants were similar to stocks is that, like stocks, shortselling was not permitted. This prevented investors who believed the warrants to be overvalued from executing short sales to take advantage of the overvaluation. 2.2 Warrant and stock information We focus on the 18 put warrants in which Xiong and Yu (2011) document the existence of a speculative asset price bubble. Like Xiong and Yu (2011), we obtain the warrant daily price and volume, intraday price and volume, numbers of warrants issued, trading period, exercise period, strike price, and exercise ratio, from CSMAR. We obtain daily and intra-day stock price and trading volumes from the same source. We also checked some of the CSMAR data by obtaining data from a different Chinese financial data vendor, RESSET. Panels A and B of Table 1 provide some information about the put warrants, include the beginning and end of their trading periods, their terms, and their average prices, daily turnover, and daily trading volume. 2.3 Brokerage account data The main data we use are the trading records of a large set of investors who traded the put warrants. We obtain these data from a comprehensive set of brokerage account records from a securities firm in the People's Republic of China. The brokerage account records come from a total of 42 branch offices located in 17 different regions across China where a region can be either a province (e.g., Fujian), a municipality (e.g., Shanghai), or autonomous region (e.g., Xinjiang). Some of the brokerage customers traded the put warrants, among other securities, and we analyze the records of the put warrant trades. In China, individuals are restricted to have only one brokerage account, and are required to present their national identity cards when opening a brokerage account. This on its face would seem to rule out having multiple brokerage accounts. However, it is possible for one individual to control multiple brokerage accounts by gathering identity cards from friends or neighbors and opening brokerage accounts in their names. To address this, we combine the records from brokerage accounts that share the same funding account, which is an internal securities firm code that links a single individual to one or more brokerage accounts. Therefore, the unit of our analysis 7

10 is the funding account, and multiple brokerage accounts linking to the same funding account are treated as a single investor. We identify a total of 5,692,241 put warrant trades from November 23, 2005, the date when the first put warrant was listed, to December 31, 2009, the end of the data. There were 81,811 investors who traded put warrants, consisting of 80,089 individual investors and 1,722 institutional investors. These institutional investors are not large financial institutions such as mutual funds, as large institutional investors typically have direct access to the exchanges and do not trade through brokerage firms. Many and perhaps most of the institutional investors in the brokerage firm data are likely to be privately held companies. Many investors held and traded more than one warrant at the same time. Investors traded an average of 4.9 different warrants. Individuals who traded the put warrants executed a total of 69.3 purchase transactions, on average, lower than the institutional investors average of One component of Shiller s feedback look theory, positive feedback trading, speaks to purchases and sales of transactions. For example, if an investor experiences a gain from previous trading, the probability that the investor reenters the market is higher. But in actual data, an investor might use multiple buys to build up a position, and then liquidate the position using multiple sell orders. This raises the issue of how to treat sets of transactions in which multiple buys or sells are used to build up or liquidate a position. A similar issue arises in empirical analyses of the disposition effect. We resolve this issue by introducing a notion of a transaction cycle. Starting from a holding of zero units of warrant k, a transaction cycle begins with a purchase of some non-zero amount of warrant k. It then continues through possibly multiple purchases and sales, until the investor s position in warrant k returns to zero. This ends a single transaction cycle, which we treat as a single transaction. The length of the transaction cycle is the time elapsed from the first purchase that begins the cycle to the last sale that ends it. In the case that investors open and close positions on warrant k more than once within the same day, we treat these transactions as a single cycle. The rationale for this treatment is that we want to study the impact of an exogenous shock on investors positive feedback trading, which is an important mechanism in Shiller s theory, and at times we use date fixed effects to capture the effect of the shock. Therefore, we do not allow multiple transactions within a single day. The return to a transaction cycle is the weighted sum of the sale prices, weighted by the 8

11 quantities sold in the various sells, divided by the weighted sum of the purchase prices, where the weights are the quantities purchased in the various buys, minus one. We define a new investor in warrant k on date t as one who executes his or her first trade in warrant k on date t. We define a reentry investor in warrant k on date t as one who trades in warrant k before date t and opens a new transaction cycle on date t. Panel C in Table I reports the numbers of investors trading each of the 18 put warrants and the average length of the transaction cycles. The majority of transaction cycles are completed ones and there are only a small portion of uncompleted cycles, which occur when investors open a position and hold it until the warrant expiration day or the last date in our dataset. 3. The May 30, 2007 Precipitating Event Of the18 put warrants, 12 expired prior to May 30, 2007 and one was issued in June 2007, leaving five that were trading on May 30, Panels A-E of Figure I show the daily closing prices (black line, right-hand axis) and turnover (dashed blue line, left-hand axis) of these five warrants for a six-month period roughly centered on May 30, 2007, that is the months March through August, The five panels clearly show that turnover increased remarkably on May 30. For the five warrants, the ratios of the turnover on May 30 to the turnover on May 29 are 19.11, 12.72, 11.70, 3.47, and The average of these five ratios is 12.34, that is on average there was a more than 12-fold increase in turnover on May 30, The visual impression is of discontinuous changes on that date. Turnover remained high after May 30; while the turnovers of the Hualing, Wuliang, and Zhongji put warrants declined from their peaks in early June, the turnovers remained above the levels prior to May 30. Jiafei s turnover drops through the middle of June and then picks up again prior to the last trading date of June 22, 2007, at which point the series ends. Zhaohang s turnover generally declines until the middle of August, at which point it increases again prior to the last trading date of August 24, For all five warrants turnover was much more variable after May 30 than it was prior to May 30. Prices of all five warrants were reasonably stable prior to May 30, 2007, rose sharply for a few days starting on May 30, and were highly volatile after May 30. The prices of Hualing, Wuliang, and Zhongji declined from the middle of June through early July and then rebounded somewhat, always remaining well above their prices prior to May 30. Panels A-E of Figure II use the brokerage account data to show that both new and returning investors increased their trading on May 30, Specifically, each panel shows the daily closing 9

12 price (black line, right-hand axis), the number of new investors on each date (dashed blue line, left-hand axis), and the number of returning investors on each date (dotted red line, left-hand axis). A new investor in warrant k on date t is one who has not previously traded warrant k, while a returning investor is one who has previously traded warrant k. The five panels show that for all five put warrants the numbers of both new and returning investors jumped sharply on May 30. Similar to the changes in turnover shown in Figure I, the visual impression is of discontinuous changes. 5 Table II provides additional evidence to verify that the bubble was more pronounced after May 30, 2007 than before. The three panels report several statistics related to the severity of the bubble for three different combinations of warrants and time periods. The statistics are the average and maximum daily turnover; the average and maximum bubble size, where the bubble size is the difference between the warrant closing price and an estimate of the warrant fundamental value computed using the Black-Scholes formula, and the average and maximum volatility computed from intra-day five minute returns. Panel A reports these statistics for the 12 warrants that expired before May 30, 2007, Panel B reports them for the period prior to May 30 for the five warrants that traded both before and after May 30, and Panel C reports them for the period on and after May 30 for the five warrants that traded after May 30 and a sixth warrant (Nanhang) that was issued in June Comparison of the results in the Panels A and B of Table II to those in Panel C show that the bubble was much more pronounced after May 30, 2007 than before. The average bubble sizes in Panel A for the 12 warrants that expired before May 30 range from yuan (Huchang) to yuan (Haier), and the average bubble size in Panel B for the five warrants that traded both before and after May 30, 2007 during the period before May 30 ranged from yuan (Hualing) to yuan (Jiafei). In contrast, in Panel C the average bubble size after May 30 ranged from yuan (Zhaohan) to yuan (Jiafei). The average daily turnover and volatility are also much greater after May 30 than before. 5 Sections 4 and 5 below report the results of various regression models that provide evidence of both positive feedback trading and social contagion. The date fixed effects in these regression models are large and significant starting on May 30, This provides additional evidence of an important event on May 30, even controlling for the impact of other covariates. 10

13 Something important happened on May 30, The more than 12-fold increase in turnover on May 30, and the jump in the purchases by both new and returning investors, pins down the date exactly. The fact that put warrant trading volume and volatility were high starting from the opening of trading on May 30 indicates that the precipitating event happened sometime between the close of trading on May 29 and the opening on May 30. What happened before the opening of trading on May 30? Prior to May 30, 2007, a stock transaction tax of 0.1% of the value of the shares transacted was imposed on each side of a stock transaction, for a total tax of 0.2%. Warrants were exempt from the tax and also exempt from the requirement that a stock be held for at least one overnight period in the practice referred to as t + 1 settlement, making them attractive to investors interested in short-term speculation. The Chinese regulatory authorities had become concerned about the boom in stock prices, and there were rumors that they would attempt to dampen the boom by increasing the transaction tax. At about midnight on May 29 the Ministry of Finance announced a tripling of the transaction tax to 0.3% of the value transacted on each side of a transaction, for a total of 0.6%, effective immediately at the opening of trading on May The transaction tax was clearly important for the stock market. It had an immediate and substantial negative impact, with the Shanghai and Shenzhen stock indexes falling by 6.15% and 5.78%, respectively, on May 30. It may have also brought attention to the put warrants, because at the time they were the only instruments with payoffs negatively related to stock prices that were available for trading. However, it did not have any material impact on the put warrants fundamental values. The warrants were so far out of the money on May 29 that any plausible estimates of the Black-Scholes fundamental values of the put warrants were still close to zero even after the May 30 decline in stock prices. Further, the tax change did not directly impact the warrants, as the transaction tax on warrant trades was always zero. But the increase in the tax on stock trades did increase the relative attractiveness of the warrants for short term speculation, because they (along with the call warrants) were the only listed financial instruments that were exempt from the tax. The nearly discontinuous change in trading and turnover on May 30, 2007, combined with the lack of other market news relevant to the put warrants, makes it clear that this was the precipitating event that caused the extreme phase of the put warrants bubble. 6 website of Ministry of Finance. 11

14 Interestingly, the fact that there was no change in the transaction tax on warrant trades is consistent with Shiller's argument that the precipitating event need not be related to the fundamentals of the asset in which it triggers a bubble. For example, Shiller argues that the spectacular U.S. corporate earnings growth in 1994, 1995, and 1996 was a precipitating factor for the technology bubble even though the earnings growth in fact had little to do with the internet and it could not have been the Internet that caused the growth in profits [because] the fledgling Internet companies were not making much of a profit yet (Shiller 2015, p. 42). Similarly, some of the other technology bubble precipitating factors that Shiller cites, for example the growth in media reporting of business news, the expansion of defined contribution pension plans, and the growth in mutual funds were not directly related to the fundamentals of technology companies. The latter two factors however plausibly created increased demand for the stocks of technology companies, similar to how the Chinese stock transaction tax created additional demand for warrants. Looking at the comparative stability of the warrant prices before May 30 in Figures I and II, one wonders if the bubble would have received much attention absent the increase in its magnitude due to the May 30, 2007 increase in the stock transaction tax. 4 Positive Feedback Trading The second component of Shiller s feedback loop theory of speculative bubbles is positive feedback trading in which an investor is more likely to trade again if his or her past returns were positive. As shown by Daniel, Hirshleifer, and Subrahmanyam (1998) and discussed by Shiller (2003), the psychological principle of biased self-attribution can promote positive feedback trading because it leads people to attribute their past success to skill rather than luck, making them more likely to trade again. We explore feedback trading by estimating Cox proportional hazard models of the probability of a subsequent purchase of warrant k by an existing investor who has previously completed at least one transaction cycle in warrant k, that is we model the reentry of investors into warrant k. The covariates of main interest are the investor s returns on his or her previous purchases of warrant k, and, to allow for a discontinuity at a return of zero, dummy variables that take the value one if the investor s return was positive. We use a proportional hazards model because its specification takes account of the time that has elapsed since an investor completed the last 12

15 transaction cycle. Specifically, consider an investor A who had a large positive return yesterday and another investor B who had a large positive return three months ago but has not yet traded again. Investor A is more likely to trade on date t than investor B, who has probably left the warrant market and is unlikely to trade on date t. The proportional hazards model specifies that,,, the hazard function of starting a new transaction cycle for existing investor i in warrant k at day t, trading days after the end of the investor s last transaction cycle, takes the form,,,,, (1) where is the baseline hazard rate and,, is a vector of covariates that proportionally shift the baseline hazard. For investors who have previously completed one transactions cycle,, is given by,, 1 1,, 2 I 1,, 0 Controls (2) where 1,, is the return of the most recent transaction cycle of investor i in warrant k before date t. The dummy variable I 1,, 0 takes the value one if _ 1,, 0, and otherwise is zero; it allows for the possibility of a discontinuity at a return of zero. The variables, and are time to maturity, warrant, and date fixed effects, respectively. The control variables include two lags of WarrantReturnk,t, the daily market return of warrant k on date t, two lags of Turnoverk,t, the market trading volume in warrant k on date t divided by number of warrants outstanding on date t, and one lag of AdjustedFundamentalk,t, which is an estimate of the fundamental value of warrant k on date t computed as /. We use the adjusted fundamental value rather than the Black-Scholes value because we hypothesize that investors should be more sensitive to the difference between the underlying stock price and the strike price when making an investment decision in warrant k than the warrant s Black-Scholes value, which is less accessible to investors. The model also includes both remaining time to maturity and date fixed effects. The results in the previous section indicate that date fixed effects are important around and shortly after May 30, 2007; we include them for all dates to allow for the possibility that they are important on other dates as well. Time to maturity fixed effects are included because, as noted by Xiong and Yu (2011), 13

16 warrant turnover tends to increase as the maturity date approaches, which suggests that hazard rates become larger as the maturity date approaches. The warrant fixed effects allow for the possibility that hazard rates differ across warrants for reasons that are not captured by the other variables. The feedback loop theory implies that the coefficient on the return on the investor s previous transaction cycle should be greater than zero. Also, if the coefficient 2 on the dummy variable for a positive transaction cycle return is non-zero, we expect it to be positive. The specification for investors who have previously completed two or more cycles is similar to the one-cycle model, except that we add the variables 2,, and I( 2,, 0 ) to the model to capture the effect from the returns on the earlier transaction cycles, where 2,, is the average return of the transaction cycles of investor i in warrant k prior to the most recent transaction cycle before date t. We estimate the models using the partial likelihood method (Cox 1972). The estimation results are reported in Table III, and show that positive returns on previous transaction cycles predict higher probabilities that investors open a new transaction cycles for both versions of the model. The coefficients on ReturnLag1 are large and highly significant, with p-values less The coefficient on ReturnLag2 in the second model is smaller, as expected, and highly significant, with a p-value less than as well. Additionally, the estimated coefficient 2 on the dummy variable for a positive return is large and highly significant, indicating that a warrant investor is more likely to return to the market if his or her previous warrant return was positive. These results indicate the presence of positive feedback trading. The estimated coefficients on the control variables also have the expected signs, with varying but generally very high levels of statistical significance. Figure III plots the calendar date fixed effects for a four-month window approximately centered on May 30, One can see an obvious jump on May 30, capturing the direct effect of the increased transaction tax on existing investors reentry into the warrant market. This is consistent with the conclusion in the preceding section that the tripling of the stock transaction tax had an important effect on the warrant market. The immediate large increase in warrant prices on May 30, 2007 due to the transaction tax, combined with the positive coefficients on lagged returns in the hazard rate model, suggest that positive feedback trading might have been important during the days following May 30. To 14

17 explore this further, for each trading date t we calculate the fitted investor reentry probability in warrant k on date t as,, 1 exp exp,,. (3) We then set the previous return variables (such as 1,, and I 1,, 0 ) to zero and recalculate the reentry probability using equation (3), calling the result,,. The difference,,,, is the part of the reentry probability that is due to positive feedback. Letting Q i, k be the average trade size of investor i in warrant k in the previous cycles, the product,,,,, measures the effect of positive feedback on the trading volume of investor i in warrant k on date t. Then for each of the five warrants, on each trading date, we sum the terms,,,,, over all existing one-cycle investors i, yielding an estimate of the total trading volume of one-cycle investors that is due to positive feedback. The five time series, along with the corresponding quantities for the two-cycle investors which we compute in a similar way, are plotted in Figure IV. One can see clearly that the effect of positive feedback becomes important starting from May 30, Comparing Figure IV to Figures I and II, one can also see that the period when positive feedback trading was important is exactly the extreme phase of the bubble. We further pursue this issue in Section Social Contagion Various writings by Shiller, sometimes with coauthors, emphasize the role of social contagion in speculative booms and bubbles (Shiller 1984, 1990, 2010, 2015; Akerlof and Shiller 2009; Case and Shiller 1988, 2003). For example, Shiller (2015; Chapter 10) asserts that after millions of years of evolution word of mouth communication and its importance are hard-wired into our brains. He argues that people do not give other sources of information the same emotional weight, and cannot remember or use information from these other sources as well. Relatedly, Shiller (2010; p. 41) claims that the single most important element to be reckoned in understanding any speculative boom is the social contagion of boom thinking. Recently, Shive (2010) and Kaustia and Knüpfer (2012) have used Finnish data to study the effect of social contagion on purchases of individual stocks and the decision to enter the stock market, respectively. Kaustia and Knüpfer (2012) focus on distinguishing between two plausible channels by which stock market outcomes of peers might influence individuals entry decisions. 15

18 In the first channel, individuals might use peer outcomes to update beliefs about long-term fundamentals, such as the equity premium. In the second channel, people cannot directly observe peer outcomes and rely on word of mouth verbal accounts and possibly other indirect information. Such verbal accounts are likely be biased toward reporting positive outcomes, as investors are unlikely to benefit from discussing their negative outcomes with their peers. As Kaustia and Knüpfer (2012) discuss, investors might enjoy discussing their positive stock market experiences more than their negative ones. Second, appearing to be a competent investor might carry private benefits. Third, various theories in psychology predict that people have self-serving biases in recalling and interpreting the factors involved in their successes and failures. To the extent such selective reporting is present, peer outcomes will have a stronger influence on the entry of new investors when the outcomes have been better. Kaustia and Knüpfer (2012) distinguish between the two channels by estimating panel regression models explaining the entry of new stock market investors in which the key variables of interest are transformations of the previous month s average return experienced by investors in the same postal code, as other investors sharing an investor s postal code are those most likely to interact with and influence the entry decision of an investor. Kaustia and Knüpfer (2012) find that the lagged average return affects entry decisions when it is positive, but it unrelated to entry decisions when it is negative. This is consistent with selective reporting and peer returns affecting entry via word of mouth communication. We also look for evidence of social contagion by estimating panel regression models that explain the entry of new investors in the warrant market. An investor who trades warrant k on date t is considered a new investor in warrant k on date t if date t is the first day that he or she trades warrant k. The unit of observation is branch-warrant-day. Similar to Kaustia and Knüpfer (2012), in our regression models the key variables of interest are transformations of the past returns of other local investors, though in our case the other local investors are those who trade through the same brokerage firm branch office rather than those who share the same postal code. A potential warrant investor is more likely to have social interactions and word-of-mouth communication with other investors who trade using the same branch office, as two investors trading at the same branch office are more likely to live and/or work near each other than are two investors trading through different branch offices. In larger cities in which the brokerage firm has multiple branch offices trading through the same branch office is a proxy for living and/or working in the same or a nearby 16

19 district. In smaller cities in which the brokerage firm has only one branch office trading through the same branch office is a proxy for living and working in the same city. For each branch-warrant-day in the dataset we construct two variables BranchAveragePosReturnjkt and BranchAverageNegReturnjkt, which are the averages of the positive and negative parts of the returns of the branch j investors who have positions in warrant k on date t, respectively. As discussed above the motivation for these two variables is that social contagion effects via word-of-mouth communication are likely to be stronger if other branch j investors have experienced positive returns in warrant k, because investors are more likely to discuss their past investment successes with their friends and colleagues than their past failures. In contrast, the performance of investors who trade at other branches is less likely to affect the entry of branch j investors into the warrant market. To compute the variables BranchAveragePosReturnjkt and BranchAverageNegReturnjkt we consider the trades and positions of all branch j investors who either traded or held warrant k on day t. For each such investor i in warrant k on date t, we first compute Xikt, equal to the sum of: (a) the value of the position in warrant k held by investor i at the close of trading on day t 1, where the value is the product of the t 1 closing price and the number of warrants held; and (b) the value of all warrants purchased during day t, where the value is the product of the purchase price and the quantity. Second, we compute Yikt, equal to the sum of: (c) the value of the position in warrant k that investor i held at the close of trading on day t, where the value is the product of the day t closing price and the number of warrants held; and (d) the value of the warrants sold during day t, where the value is the product of the sale price and the number of warrants sold. The day t return for the investor i in warrant k is then defined as rikt = Yikt/Xikt 1. The branch j warrant k day t variable BranchAveragePosReturnjkt (BranchAverageNegReturnjkt) is then the average of the positive parts max[rikt,0] (the negative parts min[rikt,0]) over the branch j investors that either traded or held put warrant k on day t. We include up to two lags of the variables in the regression specifications, that is we explain the number of new investors on date t using the variables for dates t 1 and t 2. We expect to obtain positive coefficient estimates on the first lag of the variable BranchAveragePosReturnjkt, and non-negative coefficients on the second lag when it is included, and we expect the estimated coefficient on the lags of BranchAverageNegReturnjkt to be smaller than the coefficients on the same lags of BranchAveragePosReturnjkt.. 17